Mathematical Model May Provide Insight into How We Sense

The individual cells responsible for responding to sensory inputs--the strong scent of a flower, the light touch of a spring breeze--can cope with only a small amount of input. Yet the human ear can hear and process sounds ranging from a pin drop to the roar of a jet engine. Scientists have struggled to account for how this individually narrow range combines in a network to produce the wide range of sensed experience. Now physicists have shown how the mathematical models that describe phase transitions in physical systems might also explain our capacity to hear, see, smell, taste and touch.

Mauro Copelli of the Federal University of Pernambuco and Osame Kinouchi of the University of Sao Paulo in Brazil used a mathematical formula to show how a random network of "excitable elements," such as neurons or axons, have a collective response that is both exquisitely sensitive and broad in scope. When subtle stimuli hit the network, sensitivity is improved because of the ability of one neuron to excite its neighbor. When strong stimuli hit the network, the response is similarly strong, following what are known as power laws--mathematical relationships that do not vary with scale.

But although a mathematical model seems to fit a natural phenomenon it does not necessarily follow that the two are actually related, according to some scientists. In a paper published last September in BioEssays, Evelyn Fox Keller of the Massachusetts Institute of Technology explained that just because mathematical models help explain physical systems, like the density of a gas, it does not mean that they also apply to biological systems, even if they seem to fit. "Fitting available data to such distributions is suspiciously easy," she wrote. "Even when the fit is robust, it adds little if anything to our knowledge of the actual architecture of the network."

Time--and experiments--will tell. Copelli and Kinouchi point to one experiment that might prove or disprove their hypothesis. Tests of mice genetically engineered to lack a protein that facilitates electrical connections between cells have shown that they do not see as well. The Brazilian physicists predict that they will not hear as well either. The paper was published yesterday in Nature Physics.

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